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Computer Science  | enregistrements trouvés : 97

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I will describe a recent framework for robust shape reconstruction based on optimal transportation between measures, where the input measurements are seen as distribution of masses. In addition to robustness to defect-laden point sets (hampered with noise and outliers), this approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries.

68Rxx ; 65D17 ; 65D18

We will cover some of the more important results from commutative and noncommutative algebra as far as applications to automatic sequences, pattern avoidance, and related areas. Well give an overview of some applications of these areas to the study of automatic and regular sequences and combinatorics on words.

11B85 ; 68Q45 ; 68R15

Tous les fournisseurs d'applications mettent actuellement en place des infrastructures "cloud". Cette nouvelle approche de l'utilisation des logiciels va complètement changer notre comportement en tant qu'utilisateurs, mais aussi en tant qu'enseignants et en tant que chercheurs.
L'objectif de cet exposé est de dégager les grands concepts scientifiques de cette évolution technologique et commerciale.
* Pourquoi le cloud aujourd'hui?
* Qu'est-ce qui a permis son émergence si rapide maintenant?
* Qu'est-ce que ça change pour l'enseignement?
* Quels sont les nouveaux défis de recherche qui sont posés?
Tous les fournisseurs d'applications mettent actuellement en place des infrastructures "cloud". Cette nouvelle approche de l'utilisation des logiciels va complètement changer notre comportement en tant qu'utilisateurs, mais aussi en tant qu'enseignants et en tant que chercheurs.
L'objectif de cet exposé est de dégager les grands concepts scientifiques de cette évolution technologique et commerciale.
* Pourquoi le cloud aujourd'hui?
* Qu'est-ce ...

68Qxx

La décomposition par substitution des permutations permet de voir ces objets combinatoires comme des arbres. Je présenterai d'abord cette décomposition par substitution, et les arbres sous-jacents, appelés arbres de décomposition. Puis j'exposerai une méthode, complètement algorithmique et reposant sur les arbres de décomposition, qui permet de calculer des spécifications combinatoires de classes de permutations à motifs interdits. La connaissance de telles spécifications combinatoires ouvre de nouvelles perspectives pour l'étude des classes de permutations, que je présenterai en conclusion. La décomposition par substitution des permutations permet de voir ces objets combinatoires comme des arbres. Je présenterai d'abord cette décomposition par substitution, et les arbres sous-jacents, appelés arbres de décomposition. Puis j'exposerai une méthode, complètement algorithmique et reposant sur les arbres de décomposition, qui permet de calculer des spécifications combinatoires de classes de permutations à motifs interdits. La c...

68-06 ; 05A05

The performance of numerical algorithms, both regarding stability and complexity, can be understood in a unified way in terms of condition numbers. This requires to identify the appropriate geometric settings and to characterize condition in geometric ways.
A probabilistic analysis of numerical algorithms can be reduced to a corresponding analysis of condition numbers, which leads to fascinating problems of geometric probability and integral geometry. The most well known example is Smale's 17th problem, which asks to find a solution of a given system of n complex homogeneous polynomial equations in $n$ + 1 unknowns. This problem can be solved in average (and even smoothed) polynomial time.
In the course we will explain the concepts necessary to state and solve Smale's 17th problem. We also show how these ideas lead to new numerical algorithms for computing eigenpairs of matrices that provably run in average polynomial time. Making these algorithms more efficient or adapting them to structured settings are challenging and rewarding research problems. We intend to address some of these issues at the end of the course.
The performance of numerical algorithms, both regarding stability and complexity, can be understood in a unified way in terms of condition numbers. This requires to identify the appropriate geometric settings and to characterize condition in geometric ways.
A probabilistic analysis of numerical algorithms can be reduced to a corresponding analysis of condition numbers, which leads to fascinating problems of geometric probability and integral ...

65F35 ; 65K05 ; 68Q15 ; 15A12 ; 65F10 ; 90C51 ; 65H10

Post-edited  Une deuxième révolution galiléenne ?
Dowek, Gilles (Auteur de la Conférence) | CIRM (Editeur )

L'introduction d'un nouveau concept scientifique permet souvent de donner de nouvelles réponses à des questions anciennes qui n'avaient jusqu'alors reçu que des réponses imparfaites. Cet exposé présente quelques questions qui ont trouvé de nouvelles réponses depuis que nous comprenons mieux la notion d'algorithme : qu'est-ce qu'un aéroport ?, qu'est-ce qu'une cellule, qu'est-ce qu'une loi physique ?, ... La prise de conscience du caractère algorithmique de ces objets scientifiques nous amène à considérer de nouveaux langages pour les décrire. Cette révolution, dans le langage dans lequel la science s'écrit, peut-être comparée à la révolution qui s'est produite, au début du XVIIe siècle, quand le langage mathématique a commencé à être utilisé pour décrire des phénomènes physiques. L'introduction d'un nouveau concept scientifique permet souvent de donner de nouvelles réponses à des questions anciennes qui n'avaient jusqu'alors reçu que des réponses imparfaites. Cet exposé présente quelques questions qui ont trouvé de nouvelles réponses depuis que nous comprenons mieux la notion d'algorithme : qu'est-ce qu'un aéroport ?, qu'est-ce qu'une cellule, qu'est-ce qu'une loi physique ?, ... La prise de conscience du caractère ...

00A30 ; 03B35 ; 68T15

Post-edited  Coloring graphs on surfaces
Esperet, Louis (Auteur de la Conférence) | CIRM (Editeur )

Post-edited  Le problème Graph Motif - Partie 1
Fertin, Guillaume (Auteur de la Conférence) | CIRM (Editeur )

Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des réseaux biologiques, comme par exemple des réseaux d'interaction de protéines ou des réseaux métaboliques. Graph Motif a fait depuis l'objet d'une attention particulière qui se traduit par un nombre relativement élevé de publications, essentiellement orientées autour de sa complexité algorithmique.
Je présenterai un certain nombre de résultats algorithmiques concernant le problème Graph Motif, en particulier des résultats de FPT (Fixed-Parameter Tractability), ainsi que des bornes inférieures de complexité algorithmique.
Ceci m'amènera à détailler diverses techniques de preuves dont certaines sont plutôt originales, et qui seront je l'espère d'intérêt pour le public.
Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des ...

05C15 ; 05C85 ; 05C90 ; 68Q17 ; 68Q25 ; 68R10 ; 92C42 ; 92D20

We will consider (sub)shifts with complexity such that the difference from $n$ to $n+1$ is constant for all large $n$. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most $d/2$ ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss further improvements when more assumptions are allowed. This is ongoing work with Michael Damron. We will consider (sub)shifts with complexity such that the difference from $n$ to $n+1$ is constant for all large $n$. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most $d/2$ ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss ...

37B10 ; 37A25 ; 68R15

The alternating direction method of multipliers (ADMM) is an optimization tool of choice for several imaging inverse problems, namely due its flexibility, modularity, and efficiency. In this talk, I will begin by reviewing our earlier work on using ADMM to deal with classical problems such as deconvolution, inpainting, compressive imaging, and how we have exploited its flexibility to deal with different noise models, including Gaussian, Poissonian, and multiplicative, and with several types of regularizers (TV, frame-based analysis, synthesis, or combinations thereof). I will then describe more recent work on using ADMM for other problems, namely blind deconvolution and image segmentation, as well as very recent work where ADMM is used with plug-in learned denoisers to achieve state-of-the-art results in class-specific image deconvolution. Finally, on the theoretical front, I will describe very recent work on tackling the infamous problem of how to adjust the penalty parameter of ADMM. The alternating direction method of multipliers (ADMM) is an optimization tool of choice for several imaging inverse problems, namely due its flexibility, modularity, and efficiency. In this talk, I will begin by reviewing our earlier work on using ADMM to deal with classical problems such as deconvolution, inpainting, compressive imaging, and how we have exploited its flexibility to deal with different noise models, including Gaussian, ...

65J22 ; 65K10 ; 65T60 ; 94A08

We show that two-player stochastic games with perfect-information and shift-invariant submixing payoff functions are half-positional, i.e. in these games the maximizer has a positional optimal strategy. This extension of our previous result for one-player games relies on an interesting existence result about the existence of epsilon-subgame-perfect strategies.

68Q60 ; 91AXX

We present two related contributions of independent interest: high-probability finite sample rates for $k$-NN density estimation, and practical mode estimators ­ based on $k$-NN ­ which attain minimax-optimal rates under surprisingly general distributional conditions.

$k$-nearest neighbor ($k$-NN) - $k$-NN density rates - mode estimation

62G07

A non-backtracking walk on a graph is a directed path such that no edge is the inverse of its preceding edge. The non-backtracking matrix of a graph is indexed by its directed edges and can be used to count non-backtracking walks of a given length. It has been used recently in the context of community detection and has appeared previously in connection with the Ihara zeta function and in some generalizations of Ramanujan graphs. In this work, we study the largest eigenvalues of the non-backtracking matrix of the Erdos-Renyi random graph and of the Stochastic Block Model in the regime where the number of edges is proportional to the number of vertices. Our results confirm the "spectral redemption" conjecture that community detection can be made on the basis of the leading eigenvectors above the feasibility threshold. A non-backtracking walk on a graph is a directed path such that no edge is the inverse of its preceding edge. The non-backtracking matrix of a graph is indexed by its directed edges and can be used to count non-backtracking walks of a given length. It has been used recently in the context of community detection and has appeared previously in connection with the Ihara zeta function and in some generalizations of Ramanujan graphs. In this work, we ...

05C50 ; 05C80 ; 68T05 ; 91D30

Post-edited  Wrapping in exact real arithmetic
Müller, Norbert (Auteur de la Conférence) | CIRM (Editeur )

A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models.
In TTE Taylor models have not been considered explicitly, as they use would not change the induced computability, already established using ordinary interval computations. However for the viewpoint of efficiency, they lead to significant improvements.
In the talk we report on recent improvements on the iRRAM software for exact real arithmetic (ERA) based on Taylor models. The techniques discussed should also easily be applicable to other software for exact real computations as long as they also are based on interval arithmetic.
As instructive examples we consider the one-dimensional logistic map and a few further discrete dynamical systems of higher dimensions
Joint work with Franz Brauße, Trier, and Margarita Korovina, Novosibirsk.
A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models.
In TTE Taylor models have not been considered ...

68Q25 ; 03D60 ; 65Y15

De nombreux problèmes d'optimisation sont NP-complets. Nous ne connaissons pas de problème NP-complet qui admette un algorithme optimal de résolution s'exécutant en temps polynomial en la taille de l'instance (sinon P=NP serait établi), et l'intuition commune est que P =/= NP. Pour ces problèmes, la recherche de solutions optimales peut donc être prohibitive. Les algorithmes d'approximation offrent un compromis intéressant: par définition, ils s'exécutent en temps polynomial et fournissent des solutions dont la qualité est garantie. Nous introduirons la notion d'algorithme d'approximation et de schéma d'approximation en temps polynomial, et nous illustrerons ces notions sur de nombreux exemples. Nous montrerons également comment établir qu'un problème n'admet pas d'algorithme d'approximation (à moins que P=NP), ou comment établir une borne inférieure au facteur d'approximation de tout algorithme d'approximation (sauf si P=NP). De nombreux problèmes d'optimisation sont NP-complets. Nous ne connaissons pas de problème NP-complet qui admette un algorithme optimal de résolution s'exécutant en temps polynomial en la taille de l'instance (sinon P=NP serait établi), et l'intuition commune est que P =/= NP. Pour ces problèmes, la recherche de solutions optimales peut donc être prohibitive. Les algorithmes d'approximation offrent un compromis intéressant: par définition, ils ...

68W25 ; 68Q25 ; 68T20

Multi angle  New hints from the reward system
Apicella, Paul (Auteur de la Conférence) ; Loewenstein, Yonatan (Auteur de la Conférence) | CIRM (Editeur )

Start the video and click on the track button in the timeline to move to talk 1, 2 and to the discussion.

- Talk 1: Paul Apicella - Striatal dopamine and acetylcholine mechanisms involved in reward-related learning

The midbrain dopamine system has been identified as a major component of motivation and reward processing. One of its main targets is the striatum which plays an important role in motor control and learning functions. Other subcortical neurons work in parallel with dopamine neurons. In particular, striatal cholinergic interneurons participate in signaling the reward-related significance of stimuli and they may act in concert with dopamine to encode prediction error signals and control the learning of stimulus­response associations. Recent studies have revealed functional cooperativity between these two neuromodulatory systems of a complexity far greater than previously appreciated. In this talk I will review the difference and similarities between dopamine and acetylcholine reward-signaling systems, the possible nature of reward representation in each system, and discuss the involvement of striatal dopamine-acetylcholine interactions during leaning and behavior.

- Talk 2: Yonatan Loewenstein - Modeling operant learning: from synaptic plasticity to behavior

- Discussion with Paul Apicella and Yonatan Loewenstein
Start the video and click on the track button in the timeline to move to talk 1, 2 and to the discussion.

- Talk 1: Paul Apicella - Striatal dopamine and acetylcholine mechanisms involved in reward-related learning

The midbrain dopamine system has been identified as a major component of motivation and reward processing. One of its main targets is the striatum which plays an important role in motor control and learning functions. Other ...

68T05 ; 68Uxx ; 92B20 ; 92C20 ; 92C40

Subshifts of finite type are of high interest from a computational point of view, since they can be described by a finite amount of information - a set of forbidden patterns that defines the subshift - and thus decidability and algorithmic questions can be addressed. Given an SFT $X$, the simplest question one can formulate is the following: does $X$ contain a configuration? This is the so-called domino problem, or emptiness problem: for a given finitely presented group $0$, is there an algorithm that determines if the group $G$ is tilable with a finite set of tiles? In this lecture I will start with a presentation of two different proofs of the undecidability of the domino problem on $Z^2$. Then we will discuss the case of finitely generated groups. Finally, the emptiness problem for general subshifts will be tackled. Subshifts of finite type are of high interest from a computational point of view, since they can be described by a finite amount of information - a set of forbidden patterns that defines the subshift - and thus decidability and algorithmic questions can be addressed. Given an SFT $X$, the simplest question one can formulate is the following: does $X$ contain a configuration? This is the so-called domino problem, or emptiness problem: for a given ...

68Q45 ; 03B25 ; 37B50

Multi angle  Correspondants Mathrice
Azema, Laurent (Auteur de la Conférence) | CIRM (Editeur )

Les missions des correspondants Mathrice pour l'agenda, l'annuaire...

68U35

Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes over the data. Given n observations/iterations, the optimal convergence rates of these algorithms are $O(1/\sqrt{n})$ for general convex functions and reaches $O(1/n)$ for strongly-convex functions. In this tutorial, I will first present the classical results in stochastic approximation and relate them to classical optimization and statistics results. I will then show how the smoothness of loss functions may be used to design novel algorithms with improved behavior, both in theory and practice: in the ideal infinite-data setting, an efficient novel Newton-based stochastic approximation algorithm leads to a convergence rate of $O(1/n)$ without strong convexity assumptions, while in the practical finite-data setting, an appropriate combination of batch and online algorithms leads to unexpected behaviors, such as a linear convergence rate for strongly convex problems, with an iteration cost similar to stochastic gradient descent. Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this setting, online algorithms such as stochastic gradient descent which pass over the data only once, are usually preferred over batch algorithms, which require multiple passes ...

62L20 ; 68T05 ; 90C06 ; 90C25

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